RMS is a fundamental measurement of the magnitude of an alternating current (AC) signal. Defined practically, the RMS value assigned to an AC signal is the amount of DC required to produce an equivalent amount of heat in the same load. For example, an AC signal of 1 volt RMS produces the same amount of heat in a resistor as a 1 volt DC signal. Defined mathematically, the RMS value of a voltage is obtained by squaring the signal, taking the average, and then taking the square root. RMS-to-DC converters provide a DC output equal to the RMS value of an AC or fluctuating DC input. Conventionally, there are two basic techniques used in RMS-to-DC converters: explicit and implicit approaches.
The explicit method computes the RMS value of an input signal using a straight-forward approach, as depicted in FIG. 1A. The input signal is first squared by a multiplier 110. The average value is then taken by using an appropriate filter 120, and the square root is obtained using circuitry 130 containing at least an operational amplifier with a second squarer in the feedback loop. This explicit circuit has limited dynamic range because the stage following the multiplier 110 deals with a signal that varies enormously in amplitude. For example, an input signal with a dynamic range of 100 to 1 (e.g., 10 mV to 1 V) has a dynamic range of 10,000 to 1 at the output of the multiplier 110. This disadvantage thus restricts the explicit method to inputs with a limited dynamic range.
A generally better computing scheme uses feedback to perform the square root function implicitly at the input of the circuit as illustrated in FIG. 1B. The output is fed back to the direct-divide input of a multiplier 140. In this circuit, the output of the multiplier/divider 140 varies linearly with (instead of as the square of) the RMS value of the input. This approach thus considerably increases the dynamic range of the implicit circuit, as compared to the explicit circuit. Additionally, implicit RMS computation advantageously involves fewer components and thus lower cost.
In both explicit and implicit RMS-to-DC converters, however, the ideal DC output voltage that exactly equals the RMS value of its input voltage, regardless of the amplitude, frequency, or wave shape of the input waveform, is never achieved; instead, the output voltage usually contains some errors, for example, an AC component. The AC component, which may be present as a ripple waveform as depicted in FIG. 2, results from incomplete suppression of the alternating waveform shape within the RMS-to-DC converter. One approach to reducing the ripple is to use a low-pass filter having a long time constant. Since the ripple is inversely proportional to the time constant, a tenfold increase in this time constant, for example, will effect a tenfold reduction in ripple. However, using a long time constant filter also proportionally increases the settling time for a change in input level. A long settling time increases the processing time of the converter, since the converter output will take longer to adjust to a change in RMS level.
Accordingly, a more popular approach for reducing output ripple is to use a “post-filter.” A post-filter may be no more than a low-pass filter connected to the output pin of the RMS-to-DC converter. Post-conversion filtering may reduce the output ripple of a frequency higher than the cutoff frequency of the post-filter; however, the post-filter does not reduce the DC error due to finite averaging time (or averaging error) and the ripple reduction may still be insufficient for certain devices (e.g., a high-resolution analog-to-digital converter (ADC)) that require a highly certain output DC signal. Conventionally, this problem may be solved by using a multipole post-filter or two RMS-to-DC converters connected in series or in parallel; however, these approaches require a more complicated circuitry design and have extra costs associated with the second converter. Consequently, there is a need for a circuit that effectively and economically suppresses the output ripple of an RMS-to-DC converter.